Italian Premier Francesco Cossiga's minority government resigned today and amid mounting tensions caused by an escalation of terrorist violence that has taken the lives of three Italian judges since Sunday.

The three-party government -- Italy's 38th in 35 years -- resigned late this evening after a short debate in the Italian parliament during which the third-ranking Socialist Party announced it was withdrawing its support. Its backing had allowed the minority Cabinet to survive.

As the debate was proceeding in the Chamber of Deputies, terrorists belonging to the Front-Line guerrilla group killed a Milan judge, Guido Galli, 48, as he entered a university building to give a criminology lecture.

Yesterday Red Brigades terrorists in Rome murdered Girolamo Minervini, a high-ranking judge, as he rode to work on a bus.

On Sunday, the second anniversary of the kidnaping of former Premier Aldo Moro, later murdered, the Red Brigades assassinated a state prosecutor in the southern city of Salerno as he was walking with his wife and son.

Following the debate, which stopped short of a vote of no confidence, Cossiga, 51, went to the Quirinale Palace to present his government's resignation. President Alessandro Pertini is expected to begin consultations on the formation of a new government Thursday. eInformed sources said that within a few days Cossiga himself would probably be asked to try to put together a new Cabinet.

It is not expected to be easy. At present none of the possibilities -- a coalition of five, three or two parties, all which would exclude the powerful Communist Party, appears to have sufficient support. Over the negotiations looms the prospect of important nationwide regional elections in June. The posts at stake in those elections in 15 of Italy's regions are local, but local elections in Italy are known to produce significant political fallout.

The government that resigned tonight had been in office since Aug. 4. Composed of members of the ruling Christian Democratic Party, several independents and a smattering of centrist Social Democrats and Liberals, it had been formed as a "government of truce."

Its main function was to give the country a government despite the political stalemate that resulted from inconclusive general elections last June and a decision by the second-ranking Communists not to join any government that did not offer them full Cabinet posts.

A five-day congress of the Christian Democratic Party in February ended with the victory of a hard-line group that ruled out any prospect of inviting the Communists to join a future coalition.

With only 262 votes in the 630-member Chamber of Deputies, however, the Christian Democrats cannot govern alone. This means that Italy's junior Marxist party, the Socialist, holds the balance of power with 62 seats.

Last summer, acting on the basis of a spring campaign pledge to assure this country a government, the Socialists facilitated the birth of the Cossiga government by agreeing to abstain. They had always said that after the Christain Democratic congress it would be necessary to form a "real" government, that is, one based on a political agreement among coalition parties.

The next several weeks are likely to be spent in complex political negotiations that are confusing to foreign observers but which are part of Italian political practice, more akin to a Cabinet reshuffle than to a real political crisis. In the end, Italy could even end up with a one-party minority government or a minority coalition similar, though not identical, to that which resigned this evening.

In his speech to parliament this morning, Cossiga emphasized the need for political stability. Continuing inflation, now at 21 percent, a rapidly growing trade deficit, and terrorism also make a stable government a high priority, politicians from several parties said today.

Today's murder brought to 18 the number of deaths in Italy from political violence this year.